[Pw_forum] Fwd: shape of real space wave functions in wfc2kr

[Jacopo Simoni]

Ok many thanks for the reply, and sorry for the delay.

1- To check this problem I made a simple scf calculation for H atom in a
cubic cell with 8 k points and when I run wfck2r now I get nks = 8, so I do
not think it is a bug, I will try to figure out what is wrong with my other
calculation but I think there is a problem with my input
2- So you are saying that the wave functions I get are the coefficients
u_nk(r) in Psi_nk(r) = u_nk(r) e^ikr . These cannot be used to reconstruct
the density in real space because they are on the smooth grid . This smooth
grid is always given by the expression
r_ijk(:) = (i-1)/nr1x * a_1(:) + (j-1)/nr2x * a_2(:) + (k-1)/nr3x * a_3(:) ?
This function u_nk(r) does not seem to be normalized, what is the
normalization factor ? are these the same wave functions used in the
routine hpsi to compute the product with the local part of the potential ?

I am sorry for all these questions, but before using this object I want to
be sure what it is exactly. So I really appreciate your effort in answering
these question.

Jacopo Simoni
Los Alamos National Laboratory, Theoretical Division

---------- Forwarded message ----------
From: Lorenzo Paulatto <paulatz at gmail.com>
Date: 27 September 2017 at 01:36
Subject: Re: [Pw_forum] shape of real space wave functions in wfc2kr
To: Jacopo Simoni <simonij at tcd.ie>


> 1- why the number of k points (nks) is 1, even if I have in the restart
folder 8 k points ? the fact that in the code there is a cycle over nks
suggests that I can have more k points, I do not understand.
>

It isn't.. can you provide a simple example where you noticed this problem?


> 2- in my case dffts%nnr = dffts%nr1x * dffts%nr2x * dffts%nr3x, does this
mean that the total number of points in the real grid is equal to the total
number of points in the FFT grid ?
> in particular I have nr1x=nr2x=nr3x=160, with nnr=4096000, while
npwx=256119. The total number of points nnr is considerably higher than the
number of plane waves, does this mean that the plane wave grid is
supplemented with 4096000-256119=3839881 zeros, am I right ?
>

Yes, as long as we stick to g-space. Keep in mind that what is really
stored i "u" the periodic part of the wavefunction, without the exp(ikr)
envelope. Only the plane waves such that |G+k|^2 < ecutwfc (i.e. a sphere)
are used for u_k, but more are needed when doing the Fourier transform
(because you need a box, not a sphere), and even more when doing charge
density the square of wavefunctions is always computed in real space, on a
dense grid). Also, npwx is a per-processor maximum.

All these values are printed at the beginning:
     Parallelization info
     --------------------
sticks:   dense  smooth     PW     G-vecs:    dense   smooth      PW
Min         530     269     81                 8627     3055     539
Max         531     270     82                 8628     3056     542
Sum        1061     539    163                17255     6111    1081

"dense" is the charge-density grid
"smooth" is the grid of wavefunction squared (4*ecutwfc)
"PW" is the grid of wavefunctions


> 3- the real space wave function evc_r(:,1) that I obtain in output from
the invfft routine can be reconstructed on the unit cell according to the
following index notation:
> index = i + (j-1) * nr1x + (k-1) * nr2x * nr1x
> r_ijk(:) = (i-1)/nr1x * a_1(:) + (j-1)/nr2x * a_2(:) + (k-1)/nr3x * a_3(:)
> is this true or I am missing something ?




>
> I really appreciate any help about these questions. Many thanks in
advance.
>
> Jacopo Simoni
> Los Alamos National Laboratory, Theoretical division.
>
>
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